Question

question 17 (mandatory) (1 point)
determine x to the nearest tenth of a metre.
4.6 m
x
77°
6.3 m
a) 6.9 m
b) 7.5 m
c) 7.9 m
d) 6.2 m

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(x^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 4.6\), \(b = 6.3\), and \(C=77^{\circ}\).
So, \(x^{2}=4.6^{2}+6.3^{2}-2\times4.6\times6.3\times\cos(77^{\circ})\).

Step2: Calculate each term

First, \(4.6^{2}=21.16\), \(6.3^{2}=39.69\).
\(\cos(77^{\circ})\approx0.2225\).
\(2\times4.6\times6.3\times0.2225 = 2\times28.98\times0.2225=57.96\times0.2225\approx12.9\).
Then \(x^{2}=21.16 + 39.69-12.9\).

Step3: Simplify the equation

\(x^{2}=21.16+39.69 - 12.9=47.95\).

Step4: Solve for \(x\)

Take the square - root of both sides: \(x=\sqrt{47.95}\approx6.9\).

Answer:

A. \(6.9\ m\)